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Lerok [7]
3 years ago
9

At what angle does a diffraction grating produce a second-order maximum for light having a first-order maximum at 20.0 degrees?

Mathematics
1 answer:
hichkok12 [17]3 years ago
6 0

Answer:

At 43.2°.

Step-by-step explanation:

To find the angle we need to use the following equation:

d*sin(\theta) = m\lambda

Where:

d: is the separation of the grating

m: is the order of the maximum

λ: is the wavelength

θ: is the angle              

At the first-order maximum (m=1) at 20.0 degrees we have:

\frac{\lambda}{d} = \frac{sin(\theta)}{m} = \frac{sin(20.0)}{1} = 0.342

Now, to produce a second-order maximum (m=2) the angle must be:

sin(\theta) = \frac{\lambda}{d}*m

\theta = arcsin(\frac{\lambda}{d}*m) = arcsin(0.342*2) = 43.2 ^{\circ}

Therefore, the diffraction grating will produce a second-order maximum for the light at 43.2°.    

I hope it helps you!                                                        

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